Hello, I hope you're doing well. can you please help me finish this exercise? There are only 3 questions left, and it would be really appreciated.

here is what is done:

This is the context: The SM Technologies firm, specializing in the development of systems and teleprocessing, is looking for analysts capable of carrying out the computer design of complex algorithms in the field of simulation and statistics. This company first gives applicants an aptitude test, the results of which are normally distributed with an average = 73.2 and one standard deviation = 8. Write down by X, the result of the aptitude test where N(73.2;64)

These are the questions answered:

What are the chances out of 100 that an applicant, chosen at random, will have a score higher than 82.8? Looking (>82.8) P. X > 82 , 8 (>82.8)=(>82.873.28) P. X > 82 , 8 = P. Z > 82 , 8 73 , 2 8 =(>1.2) = P. Z > 1 , 2 (>1.2)=1(<1.2) P. Z > 1 , 2 = 1 P. Z < 1 , 2 =1(1,2) = 1 1 , 2 =10.8849 = 1 0 , 8849 =0.1151 = 0 , 1151 =11.51% = 11 , 51 % Therefore, the chances out of 100 that an applicant will have a result higher than 82.8 are 11.51% (0.1151).

25% of applicants who will take this aptitude test will have a result lower than or equal to what value?

25% correspond to quartile 1, so we are looking for: (1)=0.25 P. X Q 1 = 0 , 25 (173.28)=0.25 P. Z Q 1 73 , 2 8 = 0 , 25 0.25 ()=0.25 Yes = 0 , 25 =0.680.672 Yes = 0 , 68 0 , 67 2 =0.675 = 0 , 675 1 Q 1 173.28=0.675 Q 1 73 , 2 8 = 0 , 675 173.2=5.4 Q 1 73 , 2 = 5 , 4 1=67.8 Q 1 = 67 , 8 Thus, 25% of applicants will have a result less than or equal to 67.8.

and here is what is left:

questions:

What are the chances in 100 of getting a result between - 1.5 and + 1.5 ? What is the interval in which 50% of the results fall between = 73.2?

The firm hires applicants who are in the top 1%.

is the minimum result with which applicants must pass the test to have the possibility of being hired?